a. A deposit instrument offered by a bank guarantees that investors will receive a return during a three-month period that is as following: Stock Return (R) 0% 0% 10% X% of R X% of 10% An investor is planning to invest $200,000 in the instrument. Assuming that the risk-free rate of interest is (0.5 x Y + 9)% per annum, the dividend yield of the stock is 2% per annum, the volatility of the stock is 30% per annum, and the current stock price is $50. After deducting 2% of the investment as administrative fees and deducting the amount that should be invested in bond to provide principal protection for the investor, the bank will spend the rest in trading options for the investor to provide the stated returns. How many options should the bank trade? What is value of X? (9 marks)